Magnetic cloud models with bent and oblate cross-section boundaries

Abstract

Context. Magnetic clouds (MCs) are formed by magnetic flux ropes that are ejected from the Sun as coronal mass ejections. These structures generally have low plasma beta and travel through the interplanetary medium interacting with the surrounding solar wind. Thus, the dynamical evolution of the internal magnetic structure of a MC is a consequence of both the conditions of its environment and of its own dynamical laws, which are mainly dominated by magnetic forces. Aims. With in-situ observations the magnetic field is only measured along the trajectory of the spacecraft across the MC. Therefore, a magnetic model is needed to reconstruct the magnetic configuration of the encountered MC. The main aim of the present work is to extend the widely used cylindrical model to arbitrary cross-section shapes. Methods. The flux rope boundary is parametrized to account for a broad range of shapes. Then, the internal structure of the flux rope is computed by expressing the magnetic field as a series of modes of a linear force-free field. Results. We analyze the magnetic field profile along straight cuts through the flux rope, in order to simulate the spacecraft crossing through a MC. We find that the magnetic field orientation is only weakly affected by the shape of the MC boundary. Therefore, the MC axis can approximately be found by the typical methods previously used (e.g., minimum variance). The boundary shape affects the magnetic field strength most. The measurement of how much the field strength peaks along the crossing provides an estimation of the aspect ratio of the flux-rope cross-section. The asymmetry of the field strength between the front and the back of the MC, after correcting for the time evolution (i.e., its aging during the observation of the MC), provides an estimation of the cross-section global bending. A flat or/and bent cross-section requires a large anisotropy of the total pressure imposed at the MC boundary by the surrounding medium. Conclusions. The new theoretical model developed here relaxes the cylindrical symmetry hypothesis. It is designed to estimate the cross-section shape of the flux rope using the in-situ data of one spacecraft. This allows a more accurate determination of the global quantities, such as magnetic fluxes and helicity. These quantities are especially important for both linking an observed MC to its solar source and for understanding the corresponding evolution.

Does spacecraft trajectory strongly affect detection of magnetic clouds?

“…et al (2007) have shown that the ratio r Bx = B x / B is a function of the true impact parameter y/b for a variety of circular models ( means averaging along the spacecraft trajectory within the MC). Démoulin & Dasso (2009) have extended this . For a fixed y/b value, the derivation of this relation implies dp/db = (dr Bx /db)/(dr Bx,L /dp).…”

Dynamical evolution of a magnetic cloud from the Sun to 5.4 AU

“…Another estimation of the impact parameter can be done using the approximation introduced in the simplest form of Eq. (31), B x,cloud / B ≈ 1.2p/R (Démoulin & Dasso 2009b), assuming a cross section roughly circular. We obtain p/R ≈ 0.27 from this method.…”

“…Column 4 (UlyP1) shows the prediction on Ulysses using l = (ζ ACE + ζ Uly )/2 = 0.7 and m = l (i.e., an isotropic expansion in the plane perpendicular to the cloud axis). Column 5 (UlyP2) shows the prediction on Ulysses using l = 0.7 and m = 1, which corresponds to an expansion such that the cross-section of the magnetic cloud is deformed toward an oblate shape in the plane perpendicular to the cloud axis, with the major axis perpendicular to the global flow speed (e.g., Démoulin & Dasso 2009b). Column 6 (UlyP3) shows the prediction on Ulysses using l = 0.74 and m = 1, which corresponds to an expansion in the direction of the plasma main flow as observed on ACE, emulating the case in which the expansion in this direction was similar to the one observed on ACE almost all the time.…”

Magnetic Field Configuration Models and Reconstruction Methods for Interplanetary Coronal Mass Ejections

“…Farrugia et al (1993) and Farrugia, Osherovich, and Burlaga (1995) introduced a cylindrical model incorporating self-similarly expansion in two initially force-free constant-α codes, a cylindrical and a spherical models, and noted that the cylindrical configuration did not maintain the force-free state after it starts to expand. Thereafter, Shimazu and Vandas (2002) provided a modification of the mathematical formalism in order to keep the self-similarly expanding cylindrical model as force-free.…”

“…(f) Marubashi and Lepping (2007) include curvature into the classic model. rope (Owens, Merkin, and Riley, 2006;Vandas and Romashets, 2003;Vandas et al, 2006;Démoulin and Dasso, 2009); non-cylindrical flux rope fitting (Mulligan and Russell, 2001;Owens et al, 2012); torus fitting Marubashi and Lepping, 2007). The Grad-Shafranov reconstruction technique (Hu and Sonnerup, 2002;) assumes a structure in magneto-hydrostatic (MHS) equilibrium with an invariant direction, and uses the Grad-Shafranov equation to describe the magnetic field in the structure.…”